Surface effect on the self-equilibrium state and size-dependent elasticity of FCC thin films

On the {1 1 0} solid surface, surface stresses of two perpendicular directions, such as < 1 0 0 > and < 1 1 0 >, will differ. These different surface stresses cause different equilibrium strains in the < 1 0 0 > and < 1 1 0 > directions on a {1 1 0} thin film. In this paper, an analytical formulation is presented to predict the equilibrium strains of orthotropic thin films with {1 0 0}, {1 1 1} or {1 1 0} surfaces. This formulation is composed of the elastic constants of bulk materials and surface parameters such as surface stresses and surface elastic tensors. Transition metals with FCC structures (Cu, Ag, Au, Ni, Pd and Pt) are used in this study, along with a surface relaxation model that calculates surface parameters using atomistic calculations. Molecular dynamics simulations are performed and compared with the results of this suggested method, and both results show good agreement. In addition, size-dependent elastic constants are calculated analytically from the predicted equilibrium state.